Class X Session 2023-24 Question 10

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041) 

Question 10 

A quadrilateral PQRS is drawn to circumscribe a circle the tangent If PQ = 12 cm, QR = 15 cm and RS = 14 cm, then find the length of SP is

(a) 15 cm 

(b) 14 cm

(c) 12 cm 

(d) 11 cm

Explanation : 

A circle is inscribed inside the quadrilateral, such that each side of the quadrilateral is tangent to the circle. Now, in a cyclic quadrilateral, the opposite angles are supplementary

Given that PQRS is a cyclic quadrilateral, 

$$\therefore PQ+RS=QR+SP,-----(a)$$

Given that 

PQ=12 cm

QR=15 cm

RS=14 cm 

and putting eq(a)

$$\therefore 12+14=15+SP$$

$$\therefore SP=26-15$$

$$\therefore SP=11$$

Guess the Option and comment below  👇